Most people have heard of the Suzuki method, which is based on the principle that people can learn to play a musical instrument in much the same way that they learn a native language. It's hard to dispute the evidence that Suzuki is highly effective in producing talented young musicians. Critics of Suzuki, however, maintain that the method underemphasizes note reading and relies too heavily on passive listening, hampering a musician's ability to sightread and develop his or her own musical style.
I see several parallels between the objections to the Suzuki method and what I view as the inadequacy of learning language in a purely "native" manner, as a young child does. Both forms of learning rely heavily on imitation. Babies hear language spoken by their parents (or less optimally, on TV) and gradually learn to repeat those sounds. Suzuki students listen to their teachers as well as recordings of the Suzuki repertoire and attempt to duplicate the sound. The justification for this is that people must listen before they speak, and speak before they read. But an overemphasis on imitation as a method of learning leads to an underemphasis in developing the speaking (i.e. interpretation) and reading (i.e. comprehending previously unheard material) that are just as essential to music and language mastery.
In college I was in a production of a Gilbert & Sullivan operetta in which the female lead had never had any formal music training and could not read music. Nonetheless, she had a beautiful voice and an amazing ability to memorize both melody and lyrics almost instantly after hearing them. One thing that always bothered me about her performance, however, was that it was stylistically identical to that on the recording by the well-known D'Oyly Carte Opera Company, which was how she'd learned her part. She had reproduced every musical nuance, ornament, even the substitution of certain words in the libretto, and had "learned" the recording so thoroughly that she was unable to follow the director's artistic wishes. And although her singing was lovely to listen to, I found that her lack of versatility made me respect her somewhat less as a musician.
Of the languages I speak, the only one I have learned in this manner is Taiwanese, which I've spoken---almost exclusively with my parents---my entire life. I'm quite aware of a similar fragility in my ability to speak the language. I know what to say by what "sounds right", and what "sounds right" is based entirely on what I've heard most frequently. And though I am nearly fluent when it comes to conversations about food or people (the subjects most commonly discussed in my family), I once went to a political rally and found myself not understanding a word.
I do not mean to imply that I believe these learning methods are useless, simply that they are incomplete. Suzuki is, in fact, probably the only method of music instruction accessible for children under the age of five; I would never allow my daughter to learn with it if I thought the method were inherently bad. But I do feel that the merits of "native language instruction", as touted both in Suzuki and in the multitude of language products marketed to busy professionals, are easily overstated. Mastery requires not only learning by osmosis, but a true understanding of the underlying structure and concepts of the subject. While one may do well to use native language instruction as a starting point, it cannot also be the ending point.